Has the number of people becoming U.S. permanent residents or naturalized citizens actually declined, relative to the times those Fortune 500 companies were founded? As far as I can tell, it hasn't: somewhere around 1 million new permanent residencies are granted per year in the 2010s, versus ~250,000 in 1960, which is actually about twice as many relative to population (~0.3% of population annually now, up from ~0.15% in 1960). Sure, there are many more people wanting to become PRs than are granted, but immigration has been gradually expanding since the low of the 1930s/40s, not contracting.
It's true that immigration was freer prior to the 1930s, but today is better than any other time post-WW2, in terms of the % of the population that is foreign-born, the # of naturalized citizens, the # of permanent residencies granted, etc.